We explore the hypothesis that the observed FLRW cosmology admits a finite global completion and ask how this changes the prospects for testing quantum gravity. A finite overdense region embedded in a larger background can undergo gravitational collapse, providing a possible prehistory for the observed expansion. If the collapse approaches a finite quantum-supported density \( \rho_G \), positive spatial curvature permits a nonsingular bounce connecting contraction to expansion. In one realization, the late-time de Sitter horizon of the FLRW interior is identified with the Schwarzschild horizon of the exterior, providing a finite global completion without modifying the local FLRW dynamics. The central proposal of this review is that such a finite bouncing cosmology can act as a laboratory for quantum gravity. We use quadratic gravity and PT-symmetric quantum theory as concrete realizations while emphasizing that the observational strategy is more general. Within scalaron inflation, the measured CMB amplitude constrains the \( R^2 \) coupling \( \alpha \) once the primordial state, reheating history and pivot-scale mapping are specified. Large-angle CMB parity statistics can similarly be related, within a specified primordial-state model, to an effective PT-breaking amplitude \( A_{\rm PT} \). PT completion also suggests a possible connection between the arrow of time and quantum information: information inaccessible within one semiclassical branch may remain encoded in a unitary PT-complete quantum state, potentially reformulating aspects of both the Past Hypothesis and apparent information loss. The contracting phase provides a possible second source of structure, distinct from inflationary quantum fluctuations. Nonlinear structures may form before the bounce. If such relics survive, their evolved abundance and mass function could be constrained by dark matter, early supermassive black holes, lensing and gravitational-wave observations. Strong-gravity measurements provide complementary tests of candidate microscopic completions through black-hole perturbations, horizon absorption and extreme-mass-ratio inspirals whenever the relevant additional degrees of freedom lie in an observationally accessible regime. The resulting framework is therefore best regarded as a network of cross-consistency and falsification tests. Relations among \( A_s \), \( \alpha \), \( A_{\rm PT} \), \( Y_B \), \( \rho_G \), spatial curvature, relic populations and strong-gravity observables range from established model-specific results to phenomenological hypotheses that still require microscopic derivation. If these relations can be sufficiently specified, otherwise unrelated observations could over-constrain a common quantum-gravitational history. Cosmological maps, black holes and gravitational waves can be regarded as experiments performed by Nature in regimes inaccessible to terrestrial laboratories, providing an observational approach to quantum gravity complementary to microscopic theory building. A finite Universe may preserve measurable information about both its pre-Big-Bang evolution and its high-density quantum state, turning otherwise inaccessible quantum-gravitational dynamics into a potentially falsifiable observational programme.
